Gains from switching and evolutionary stability in multi-player matrix games.

In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric N-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other individuals in the group play a given strategy. As a consequence, the gain function determining the gradient of selection can be a polynomial of degree N-1. In order to deal with the intricacy of the resulting evolutionary dynamics, we make use of the theory of polynomials in Bernstein form. This theory implies a tight link between the sign pattern of the gains from switching on the one hand and the number and stability of the rest points of the replicator dynamics on the other hand. While this relationship is a general one, it is most informative if gains from switching have at most two sign changes, as is the case for most multi-player matrix games considered in the literature. We demonstrate that previous results for public goods games are easily recovered and extended using this observation. Further examples illustrate how focusing on the sign pattern of the gains from switching obviates the need for a more involved analysis.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

Evolutionary and convergence stability for continuous phenotypes in finite populations derived from two-allele models.

The evolution of a quantitative phenotype is often envisioned as a trait substitution sequence where mutant alleles repeatedly replace resident ones. In infinite populations, the invasion fitness of a mutant in this two-allele representation of the evolutionary process is used to characterize features about long-term phenotypic evolution, such as singular points, convergence stability (established from first-order effects of selection), branching points, and evolutionary stability (established from second-order effects of selection). Here, we try to characterize long-term phenotypic evolution in finite populations from this two-allele representation of the evolutionary process. We construct a stochastic model describing evolutionary dynamics at non-rare mutant allele frequency. We then derive stability conditions based on stationary average mutant frequencies in the presence of vanishing mutation rates. We find that the second-order stability condition obtained from second-order effects of selection is identical to convergence stability. Thus, in two-allele systems in finite populations, convergence stability is enough to characterize long-term evolution under the trait substitution sequence assumption. We perform individual-based simulations to confirm our analytic results.

Hybrid Multiscale Finite Volume method for two-phase flow in porous media

We present a novel hybrid (or multiphysics) algorithm, which couples pore-scale and Darcy descriptions of two-phase flow in porous media. The flow at the pore-scale is described by the Navier?Stokes equations, and the Volume of Fluid (VOF) method is used to model the evolution of the fluid?fluid interface. An extension of the Multiscale Finite Volume (MsFV) method is employed to construct the Darcy-scale problem. First, a set of local interpolators for pressure and velocity is constructed by solving the Navier?Stokes equations; then, a coarse mass-conservation problem is constructed by averaging the pore-scale velocity over the cells of a coarse grid, which act as control volumes; finally, a conservative pore-scale velocity field is reconstructed and used to advect the fluid?fluid interface. The method relies on the localization assumptions used to compute the interpolators (which are quite straightforward extensions of the standard MsFV) and on the postulate that the coarse-scale fluxes are proportional to the coarse-pressure differences. By numerical simulations of two-phase problems, we demonstrate that these assumptions provide hybrid solutions that are in good agreement with reference pore-scale solutions and are able to model the transition from stable to unstable flow regimes. Our hybrid method can naturally take advantage of several adaptive strategies and allows considering pore-scale fluxes only in some regions, while Darcy fluxes are used in the rest of the domain. Moreover, since the method relies on the assumption that the relationship between coarse-scale fluxes and pressure differences is local, it can be used as a numerical tool to investigate the limits of validity of Darcy's law and to understand the link between pore-scale quantities and their corresponding Darcy-scale variables.

Random mating with a finite number of matings.

Random mating is the null model central to population genetics. One assumption behind random mating is that individuals mate an infinite number of times. This is obviously unrealistic. Here we show that when each female mates a finite number of times, the effective size of the population is substantially decreased.

Managing the size of the Olympic Games

The last two decades have seen dramatic increases in the size and scope of the Summer Olympic Games. In many ways, London 2012 reached even higher summits than the Beijing Games in 2008. This growth is a major challenge for the Olympics and its future organizers, as it is making the Games increasingly difficult to stage and has greatly reduced the number of cities capable of hosting them. This study shows how various participation and organization indicators have expanded over six Olympiads, from Barcelona 1992 to London 2012, and examines the reasons for this growth. It suggests ways of reducing the size of the Summer Olympic Games in order to make them more manageable and to encourage candidatures from smaller cities and countries.

Using group role-playing games with gifted children and adolescents: A psychosocial intervention model

Gifted children develop asynchronously, often advanced for their age cognitively, but at or between their chronological and mental ages socially and emotionally (Robinson, 2008). In order to help gifted children and adolescents develop and practice social and emotional self-regulation skills, we investigated the use of an Adlerian play therapy approach during pen-and-paper role-playing games. Additionally, we used Goffman's (1961, 1974) social role identification and distance to encourage participants to experiment with new identities. Herein, we propose a psychosocial model of interactions during role-playing games based on Goffman's theory and Adlerian play therapy techniques, and suggest that role-playing games are an effective way of intervening with gifted children and adolescents to improve their intra- and interpersonal skills. We specifically targeted intrapersonal skills of exercising creativity, becoming self-aware, and setting individual goals by raising participants' awareness of their privately logical reasons for making decisions and their levels of social interest. We also targeted their needs and means of seeking significance in the group to promote collaboration and interaction skills with other gifted peers through role analysis, embracement, and distancing. We report results from a case study and conclude that role-playing games deserve more attention, both from researchers and clinical practitioners, because they encourage change while improving young clients' social and emotional development.

Religions in Play. Games, Rituals, and Virtual Worlds

Often dismissed as "not serious," the notion of play has nevertheless been at the center of classical theories of religion and ritual (Huizinga, Caillois, Turner, Staal, etc.). What can be retained of these theories for the contemporary study of religions? Can a study of "play" or "game" bring new perspectives for the study of religions? The book deals with the history of games and their relation to religions, the links between divination and games, the relations between sport and ritual, the pedagogical functions of games in religious education, and the interaction between games, media and religions. Richly illustrated, the book contributes to the study of religions, to ritual, game and media studies, and addresses an academic as well as a general public.

Development and experimental validation of a finite element model of total ankle replacement.

Total ankle replacement remains a less satisfactory solution compared to other joint replacements. The goal of this study was to develop and validate a finite element model of total ankle replacement, for future testing of hypotheses related to clinical issues. To validate the finite element model, an experimental setup was specifically developed and applied on 8 cadaveric tibias. A non-cemented press fit tibial component of a mobile bearing prosthesis was inserted into the tibias. Two extreme anterior and posterior positions of the mobile bearing insert were considered, as well as a centered one. An axial force of 2kN was applied for each insert position. Strains were measured on the bone surface using digital image correlation. Tibias were CT scanned before implantation, after implantation, and after mechanical tests and removal of the prosthesis. The finite element model replicated the experimental setup. The first CT was used to build the geometry and evaluate the mechanical properties of the tibias. The second CT was used to set the implant position. The third CT was used to assess the bone-implant interface conditions. The coefficient of determination (R-squared) between the measured and predicted strains was 0.91. Predicted bone strains were maximal around the implant keel, especially at the anterior and posterior ends. The finite element model presented here is validated for future tests using more physiological loading conditions.